Attract part of mesh around an arc
In this case, the softbodies can be used to mold the geometry to a barrier. This uses a blender simulation to fit the geometry to a barrier.






Prepare the barrier by selecting, then, in object mode, using object>apply>scale, and using the toolbar, set origin > geometry center of mass. These two changes will make it easier to apply the barrier in later steps.
Add collision physics to the barrier.





Set the timeline to an end-frame of 25. This will reduce the time required to find the final shape.





At frame 25, add a keyframe with the scale set to 1.





At frame 1, add a keyframe with the scale set to 1.2. This makes the barrier larger then the geometry and as the simulation progresses, it will press on the geometry until it reaches its final shape.





If you animate this, the barrier should shrink into the geometry. This shrinking into the geometry is how it will be shaped.





Add collision physics to the barrier.





Fix the normals so they point towards the geometry. Go to edit mode, select all, then use Mesh>Faces>Flip Normals. The softbodies iteract with the faces that have normals towards them.







Add softbody physics to the geometry to mold. There should be no other modifiers on the geometry to mold. Follow the settings shown below. Set the gravity field weight to 0. Set the cache time to 25 (this will save a lot of time on calculations).





'Bake' the soft-body physics. At the physics panel>Soft Body>Soft Body Cache>Bake. Click on Bake.





The resulting animation presses the barrier against the geometry causing it to meet that form. The last frame of the animation has the desired shape.






Blend file here: